A lion and a tiger can have offspring, despite being of a different species. I'd figure Egg Groups are a Genus. A Pokemon would be of a separate Kingdom all of their own. Phylum would be probably a Body Type. And you'd keep going down, and so on, until you hit a species, which would probably be a basic Pokemon and it's "evolutions" (or you can consider them a separate species, whatever floats your boat.) And just as separate species can, on rare cases, interbreed with other species, perhaps Pokemon have a separate biology that allows them to interbreed more readily within the same genus/families.